I am not a fan of having more than a few icons on my desktop. The Recycle Bin is one of those annoying icons that adds unnecessary clutter. There are at least three methods for removing it, and each method is easily reversible.

Method One (2000/XP Pro Only):

• Start > Run..
• Run "gpedit.msc" (opens the Group Policy Editor)
• 
  Navigate: Local Computer Policy > User Configuration > Administrative Templates > Desktop
• Right-click "Remove Recycle Bin icon from Desktop" and then click properties.
• Enable the setting (and click ok).
• Restart

Method Two (Registry Method):
To remove it, you need this Registry Patch (also included is an undelete patch). However, the Recycle Bin is still rather handy to access.

• Run the patch
• Delete the Recycle Bin

Method Three (TweakUI Required):

• Download and Install TweakUI
• Open TweakUI
• Click on "Desktop" option
• 
  Uncheck Recycle Bin
• Click Ok

Retain Usability:

• Enable Show Hidden Folders/Files
• Navigate to C:\RECYCLER
• Create a shortcut of the one item in that folder
• Move the shortcut somewhere useful.

Note: I use Josh Karlin's Launchy for all of my program launching needs. I just moved the shortcut into my "Launch" folder. This solution works equally well if you use the Start Menu or some other "non-desktop icon" method.